Dating of groundwater using uranium isotopes disequilibrium in Siwa Oasis, Western Desert, Egypt

Data on the recent migratory history of radionuclides as well as geochemical circumstances can be obtained from the disequilibrium of the uranium series, which is often brought on by groundwater flow and host rock. Groundwater from the Siwa Oasis is a vital source of water for many uses, and it is distributed widely throughout the Western Desert. Groundwater in Siwa Oasis was dated using measurements of uranium in the water. In water samples that exhibited disequilibrium behavior, the activity concentrations of radionuclides from the 238U, 235U and 232Th series were measured. Therefore we conclude that the measured waters are rich in the 234U and 230Th. The secular equilibrium between 234U and 230Th indicates that colloidal transport could be the mechanism for the mobility of 230Th in groundwater. Higher 230Th levels in the samples show that the aquifer is deep and may have a large amount of thorium-bearing minerals. The lake and groundwater estimated ages showed that the time of uranium migration happened between 60 and 130 ka ago. This aquifer is rich in mineral deposits, as evidenced by the extraordinarily high content of radionuclides. The 230Th/232Th activity ratio of the samples, indicating pure carbonate minerals, ranged from 12.58 to 20.86.


Scientific Reports
| (2023) 13:12406 | https://doi.org/10.1038/s41598-023-39333-w www.nature.com/scientificreports/ transition daughters such as 234 U and 230 Th, which have half-lives of 245,000 and 75,400 a, respectively. In this decay series, a disequilibrium between U and Th occurs when U and Th differ due to a different geographical or climatic event. The system reaches near-secular equilibrium only after seven times the half-life of Th-230 (500 Ka), after this radioactive disequilibrium has occurred. The radioactive disequilibrium between nuclides in the decay series is a marker for earlier fractionation processes, which are typically associated with the increase or decrease of highly migrating isotopes 14 . This process is described via the Bateman Eq. (1) [15][16][17] .
Here T is the age of the sample, the activity ratios are 238 U/ 234 U and 230 Th/ 234 U, and λ 230 and λ 234 are the corresponding decay constants of 230 Th and 234 U.
The age determined using the above equation is valid if the following assumptions are fulfilled (1) the U/ Th isotope system has remained closed since the U/Th fractionation event; (2) the U/Th fractionation "event" is a rapid process compared to elapsed time; and (3) the U/Th fractionation or dated material does not contain an initial inherited 230 Th at the time of formation or this initial 230 Th is small 18 . In a particular scenario of U/Th dating, one phase is assumed to contain all initial thorium (detrital fraction), while the other phase contains only thorium obtained by radioactive decay (authigenic fraction) 19 . The implications of detrital contamination could be mitigated by determining the activity of 232 Th, which occurs only in the detrital fraction but plays no role in the U-238 decay series 20 . 234 U had already decayed to 230 Th* (radiogenic) during ageing. The activity concentration of 230 Th* was determined from the total activity concentration of 230 Th subtraction Th (detrital) using Eq. (2). The uncorrected 230 Th/U age calculated from the difference between the 230 Th total activity concentration and the detrital corrected 230 Th*/U age determined from ( 230 Th*).
Consequently, for a more thorough understanding of the behavior of uranium-series radionuclides in the groundwater system of Siwa Oasis. This work aims to calculate the uranium age dating method for water by using U-series disequilibria and the activity concentration of U-series isotopes in the water of the western desert of Siwa Oasis.

Materials and methods
Geological setting and sampling. The Siwa Oasis is a large depression in the northwest of the Western Desert of Egypt at latitudes 29° 05′ 00″ N and 29° 25′ 00″ N and longitudes 25° 05′ 00″ and 26° 06′ 00″ E 21 . There are two major aquifers: the shallow aquifer (the upper Siwa) and the deepest aquifer (Nubian sandstone). Springs are located in the shallow Middle Miocene carbonates, which are completely isolated from the Nubian Sandstone (the deep aquifer) 22 . The Mesozoic and Palaeozoic periods are indicated by the thickness of the Nubian aquifer of 2600 m. Geologically, the Siwa Oasis carbonate aquifer system is primarily composed of hard limestone, with limestone occurring in some areas 23 . In January 2018, samples were collected from three freshwater springs and three hypersaline lakes in Siwa Oasis (Fig. 1). The Siwa Lakes (hypersaline lakes) are watersheds that collect water from cultivated areas and groundwater from wells and springs. More than three samples were collected at each site. The water samples were collected and filled into a plastic bottle (2L). All samples were kept in the icebox until returned to the laboratory. The maps were created using ArcGIS Pro 3.1 ® software by Esri. ArcGIS ® and ArcMapTM are the intellectual property of Esri and are used here in under license. Copyright © Esri. All right reserved. For more information about Esri ® software, please visit 24 www.nature.com/scientificreports/ Analytical techniques. The HPGe detector is a non-destructive method that has a relative efficiency of roughly 60% in comparison to the 3 × 3 NaI (Tl) crystal efficiency with a resolution (FWHM) of 1.90 keV, and peak/Compton ratio of 69.9:1 at the 1.33 MeV gamma transition of 60 Co. he detector was shielded from background radiation with a 10-cm-thick lead liner lined internally with a 2-mm-thick copper foil to absorb X-rays. The certified standard sources of IAEA, RGU -I, RGTh-I, and RGK-I provided by 25 , were used for the energy and efficiency calibration of the system, which covers the energy range of 46.53-3000 keV. The Gamma spectrum were recorded and analyzed using MAESTRO software from ORTEC, and the radioactive concentration was calculated manually using a spreadsheet (Microsoft Excel). To prevent contamination, marinelli beakers were cleaned, rinsed with diluted H 2 SO 4 , and dried before being filled with known volumes of water. The marinelli beakers have been firmly sealed within 4 weeks. In order to prevent radon leakage and ensure that the Uranium series and their progeny were in a condition of secular equilibrium. The activity concentration of radionuclides in water represented as Bq/l and the accumulation time for measuring was within 48-72 h. The activity concentration of 238 U was calculated via 234m Pa, whose the activity was determined from 1001 keV photo peaks. Gamma-ray peaks for 235 U at 143.8, 163.4, 185.7, and 205.3 keV were used to estimate its activity 26,27 . The activity concentration of 234 U was determined via 53.2 keV (after subtraction) and 120.9 keV (after the subtraction) 28 . The 67.7 keV peak was used to calculate the activity of 230 Th 29 . Gamma energies of 338.4 keV and 911.2 keV for 228 Ac, 583 keV and 2614.4 keV for 208 Tl, and 727.3 keV for 212 Bi were used to measure the activity concentration of 232 Th series. The concentrations of radionuclides were calculated using the equation of 30 . IAEA-reference materials (IAEA-443, IAEA-446, and IAEA-410) were used to confirm the accuracy and validity of the analytical data reported in this study, as showed in Table 1. The measuring system's lowest limits of detection (LLDs), which must be calculated in order to determine a minimum detection level for each sample's radionuclide content using an analytical method, were obtained by 31 . The obtained LLD values of water are 0.017, 0.01, and 0.005 Bq/l for 238 U, 232 Th, and 235 U, respectively.

Results and discussion
Environmental parameters. Summary of the physicochemical parameters of the water samples of the study area (Table 2). For hypersaline lakes, the temperature of water samples ranged from 16.5 to 19.5 °C, while for wells, it ranged from 31.2 to 53.2 °C. Groundwater flowing into the well from a hydraulically conductive fracture or aquifer will be warmer than the temperature at the gauge because temperature increases with aquifer depth, and vice versa 32 . The pH of the water samples varied from 7.42 to 7.92, with an average value of 7.68, indicating a neutral to slightly alkaline pH. The acceptable pH range for the groundwater samples of the well was within the range of (6.5-8.5) 33 . The total dissolved solid (TDS) measurement ranged from 0.8 to 198.61 g/l, with an average value 181.21 g/l for hypersaline lakes and 1.3 g/l for wells. The US Geological Survey recommends categorizing groundwater based on TDS as fresh (1000 mg/L), slightly saline (1000-3000 mg/L), moderately saline (300-10,000 mg/L), and extremely saline (10,000-35,001 mg/L) 34 . The classification of groundwater indicated that the groundwater of this study slightly salinized.   Table 3 and Fig. 2. The radionulcides concentration of 238 U, 234 U and 235 U ranged from 1.9 ± 0.49 Bq l −1 at Siwa (1) to 5.24 ± 0.90 Bq l −1 at Zietoun (1), from 11.01 ± 3.67 Bq l −1 at Spring (3) to 19.23 ± 6.41 Bq l −1 at Siwa (4) with an outlier 22.92 ± 7.64 Bq l −1 at Spring (1), and from 0.07 ± 0.05 Bq l −1 at Siwa (4) to 0.24 ± 0.14 Bq l −1 at Zietoun (1), respectively. While, the ranges of activity concentration of Thorium in the water samples were nearly narrow ranges from 12.45 to15.9 Bq l −1 for 230 Th with an outlier 6.5 ± 2.17 Bq l −1 at Spring (3) and 20.67 ± 6.89 Bq l −1 at Spring (1). Also, the activity concentration of 232 Th ranged from 0.4 ± 0.19 Bq l −1 at Spring (3) to 1.2 ± 0.37 Bq l −1 at Siwa (2). According to these results, the activity concentration of radionuclides of U-series in all water samples indicated that 234 U = > 230 Th > 238 U due to the variations in groundwater geochemical conditions brought on by water-rock interaction. The differences in the chemical and physical properties of the individual radionuclides, which affect their ability to dilute and move in water, are the main reason for the disequilibrium in the U-238 series 35 . The solubility, adsorption, desorption and precipitation of a nuclide are influenced by its chemical composition. The flow of water along a particular pathway is affected over time by fractionation due to the difference in solubility of the oxidized U isotopes compared to Th and relative to 234 U and 238 U, respectively 36 . The crystal lattice of rocks exposed to water interaction is altered by recoil displacement or oxidation, preferential mobilisation of 234 U relative to 238 U, adding or removal of U comparative to Th, and chemical fractionation of 234 Th 37 . In these samples, there is an enrichment in 234 U www.nature.com/scientificreports/ compared to 238 U in groundwater may due to the two processes: (a) the direct release of 234 Th from an aquifer mineral into solution followed by in situ decay to Uranium; or (b) the growth of a recoil damaged lattice site for 234 Th (and thus for 234 U) in aquifer mineral, which would be highly sensitive to preferential leaching 38 .
Additionally, contrary to the expectations, it is evident that the activity concentration of 230 Th was almost similar to the 234 U activity concentration. Thorium content in water is supposed to be relatively low due to low solubility, but there are a few studies that indicated the solubility of thorium in groundwater, such as the basaltic Snake River aquifer 39 , saline groundwaters from Missouri carbonates and sandstones 38 , and unconsolidated sandy aquifers 40 . According to EDTA data, Th solubility can be increased by complexing with organic ligands 36 and humic or carbonate materials 38 . Moreover, the high concentrations of 230 Th in this study are in agreement with the analysis of the groundwater of the Bahariya and Farafra oases in Egypt's Western Desert 41 . Whereas; The Th concentration in the waters of the Bahariya Oasis is more than ten times higher than the U concentration and The Farafra Oasis have an average of Th concentration that is a lower than the equivalent U levels, but still quit high compared to the worldwide averages. This extraordinary level of Thorium indicated that there are Th-rich minerals in the lowest depths of the aquifer, but not necessarily ore deposits.
This implies that the deep aquifer rocks are the source of the 230 Th, and chemical processes are coordinating the mobility of 230 Th rather than recoil processes. On the same context, the only way of released 232 Th from the aquifer minerals by weathering, and the existence of 232 Th in aquifers although a high removal processes from groundwater indicates that continual release happens 1 . The presence of Th-bearing minerals in the sandstone aquifer is confirmed by the extremely high values for the 232 Th-series in the water 42 , and the comparatively high 232 Th levels in some of the groundwaters must be the consequence of more recent desorption processes (within the past 30 years) 1 . The ranges of U and Th concentrations in these samples are significantly higher compared to those typical for groundwater 43 , and Thorium may be associated with colloids rather than in realistic media, as suggested by [ 44 ] for the aquifer waters of the Western Desert of Egypt. The Uranium and Thorium can be considered to have come from the crystalline host rocks, just like the other dissolved ions 45 .
Correlation between environmental variables (pH and TDS) and radionuclide isotopes ( 238 U, 234 U, 235 U, 230 Th, and 232 Th) are represented in (Fig. 3). According to the correlation, U-238 and U-235 had a weak negative connection with TDS and a moderately negative correlation with pH. This indicates that uranium increases with decreasing pH and TDS, but to different degrees. For this reason, the U content is higher in groundwater that has a more neutral pH, which is consistent with 46,47 . There is a weak positive correlation between Th-230, Th-232 and TDS, and a moderate positive correlation between Th-230, Th-232 and U-234 and pH. On the other hand, there is a strong positive correlation between Th-230, Th-232 and U-234 and a weak positive correlation between U-238 and U-234, which is contrary to expectations. According to these correlations, the pH value has a greater influence on the differentiation of the uranium concentration in water samples than the TDS value. Activity ratios. In closed geological systems, the activity ratios (ARs) 234 U/ 230 Th, 230 Th/ 238 U and 234 U/ 238 U appear to be equal to unity, but in these samples there are large radioactive disequilibria between U and its daughter (AR ≠ 1). For instance, the activity ratios (ARs) 234 U/ 230 Th, 230 Th/ 238 U and 234 U/ 238 U varied from 0.96 to 1.69, 1.33 to 10.60 and 2.25 to 12.82, respectively as shown in Table 4. From Fig. 4, 234 U/ 230 Th was very close to unity or hardly deviated from secular equilibrium in most of the samples except Spring (3), indicating disequilibrium. The equilibrium between 234 U and 230 Th indicates that Th-rich rocks in the aquifer have no discernible distribution pattern except that it is unexpectedly abundant in groundwater and this result is similar to the example analyzed by 41 .
As mentioned earlier, differential leaching of 234 U from the host matrix leads to variations in the activity ratio ( 234 U/ 238 U) in the aquifer 48 . The 234 U/ 238 U ratios are explained either by oxidising waters close to recharge zones, which have high 238 U contents and low 234 U/ 238 U activity ratios, or by reducing conditions, which have lower solubilities of 238 U and higher 234 U/ 238 U activity ratios.Our results argue for reducing conditions, and a-recoil processes preferentially inject 234 U into solution 38 . According to [49][50][51] , the average values of activity ratios ( 234 U/ 238 U) of groundwater ranged from 0.51 to 9.02. The 234 U/ 238 U ratio may occasionally move steadily to 5-20 in groundwater at mid-and high-latitudes of the Earth, and may even increase to 50 under certain circumstances [52][53][54] . In other words, the behaviour of uranium concentration in groundwater depends on the relationship between many variables, including pH, oxidation potential, CO 2 partial pressure, the rock matrix of the aquifer and the flow of the groundwater stream. However, the highest activity ratios of uranium represent the accumulation of 234 U due to the increasing interaction between water and rock over time 55 .
In the same context, the daughter nuclide ( 234 U) passes most actively from surface coatings (carbonates, iron oxides and clay minerals) into the water, increasing the activity ratio of uranium isotopes in water 56 . The results suggest that the uranium series disequilibrium may be an important tool for tracking the migration of uranium series radionuclides in groundwater from different aquifers 48 . The 238 U/ 235 U ratio (AR) showed no relevant variation among the samples and approached the value of the natural uranium ratio of 21.7, as shown in Fig. 4.
The Thiel diagram of 230 Th/ 238 U versus 234 U/ 238 U (Fig. 5) was used to identify the deposition or leaching (removal) of U at the sites; we rely here on Thiel's conceivable hypotheses 57 . According to this diagram, the forbidden zone contains all samples. It could be seen that the systems have difficulties that complicate uranium mobility in the forbidden zone, a complex geochemical zone. Datasets located in the forbidden zone may be caused by ongoing and conflicting uranium mobilisation activities 58 . The data set located in the forbidden zone could explain the relative rates of U gains and losses and the degree of U fractionation 59 .
Uranium-series dating. The ages of groundwater determined in this study are shown in Table 5. An important source of uncertainty in U/Th dating is the correction of thorium not grown in by radioactive decay; isochron methods are effective mechanisms for reducing these uncertainties. Almost all samples have the activ-    60 , if the 230 Th/ 232 Th activity ratio is less than 20, significant detrital contamination is assumed; the samples in this study, with the exception of Zietoun (1) and (2), were less than 20. The samples with ratios greater than 20 can be considered pure carbonate samples and correction may not be necessary. Even though our samples were corrected to determine the real age of the samples.
The slope of the straight mixing line (isochron) in the diagram of 230 Th/ 232 Th AR versus 234 U/ 232 Th (AR) corresponds to the actual 230 Th*/ 234 U (AR), which is the crucial parameter for calculating 230 Th*/U ages. The intersection of the isochron with the y-axis gives the actual [ 230 Th/ 232 Th] AR or the thorium index f 61 , as shown in Fig. 6. The isochron-corrected age of the samples corrected with a 230 Th/ 232 Th ratio was 3.91. The actual radiogenic 230 Th and the age of the investigated samples were determined using the Eq. (2). The activity concentrations of Th*(radiogenic), 230 Th/ 234 U, 238 U/ 234 U, 234 U/ 232 Th, 230 Th/ 232 Th and 230 Th*/ 234 U were used to calculate the uncorrected ages and the correct ages as shown in Table 3. Plots of the 234 U/ 238 U activity ratios versus the detrituscorrected 230 Th/ 238 U activity ratios are also used to verify the closed system conditions (Fig. 7). The uncorrected ages of the uranium deposits in the water samples studied ranged from 87.87 to 193.01 Ka and the corrected ages ranged from 61.01 to 130.99 Ka, which is lower than the values found in the groundwater of Dakhla Oasis in the Western Desert of Egypt 2 and consistent with the groundwater in the natural reference site Palmottu in Finland 37 .

Data availability
The datasets and materials used during the current study are available from the corresponding author on reasonable request. All data generated or analysed during this study are included in this published article.